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The maximum work principle regarded as a consequence of an optimization problem based on mechanical virtual power principle and application of constructal theory

Abstract : This scientific paper proposes to prove that the maximum work principle used by theory of continuum media plasticity can be regarded as a consequence of an optimization problem based on constructal theory (prof. Adrian BEJAN). It is known that the thermodynamics define the conservation of energy and the irreversibility of natural systems evolution. From mechanical point of view the first one permits to define the momentum balance equation, respectively the virtual power principle while the second one explains the tendency of all currents to flow from high to low values. According to the constructal law all finite-size system searches to evolve in such configurations that flow more and more easily over time distributing the imperfections in order to maximize entropy and to minimize the losses or dissipations. During a material forming process the application of constructal theory principles leads to the conclusion that under external loads the material flow is that which all dissipated mechanical power (deformation and friction) become minimal. On a mechanical point of view it is then possible to formulate the real state of all mechanical variables (stress, strain, strain rate) as those that minimize the total dissipated power. So between all other virtual non-equilibrium states, the real state minimizes the total dissipated power. It can be then obtained a variational minimization problem and this paper proof in a mathematical sense that starting from this formulation can be finding in a more general form the maximum work principle together with an equivalent form for the friction term. An application in the case of a plane compression of a plastic material shows the feasibility of the proposed minimization problem formulation to find analytical solution for both cases: one without friction influence and a second which take into account Tresca friction law. To valid the proposed formulation, a comparison with a classical analytical analysis based on slices, upper/lower bound methods and numerical Finite Element simulation is also presented. © 2017 Author(s).
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https://hal-univ-rennes1.archives-ouvertes.fr/hal-01671673
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Submitted on : Friday, December 22, 2017 - 2:53:55 PM
Last modification on : Monday, January 20, 2020 - 10:26:05 PM

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A. Gavrus. The maximum work principle regarded as a consequence of an optimization problem based on mechanical virtual power principle and application of constructal theory. 20th International ESAFORM Conference on Material Forming, ESAFORM 2017, Apr 2017, Dublin, Ireland. ⟨10.1063/1.5008127⟩. ⟨hal-01671673⟩

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